Fast-forwarding of Hamiltonians and exponentially precise measurements

Yosi Atia () and Dorit Aharonov
Additional contact information
Yosi Atia: The Hebrew University of Jerusalem, The Edmond J. Safra Campus
Dorit Aharonov: The Hebrew University of Jerusalem, The Edmond J. Safra Campus

Nature Communications, 2017, vol. 8, issue 1, 1-9

Abstract: Abstract The time-energy uncertainty relation (TEUR) $$\Delta {\it{t}}\Delta {\it{E}}\,{\bf{ \ge }}\,{\textstyle{{\bf{1}} \over {\bf{2}}}}$$ Δ t Δ E ≥ 1 2 holds if the Hamiltonian is completely unknown, but can be violated otherwise; here we initiate a rigorous study describing when and to what extent such violations can occur. To this end, we propose a computational version of the TEUR (cTEUR), in which Δt is replaced by the computational complexity of simulating the measurement. cTEUR violations are proved to occur if and only if the Hamiltonian can be fast forwarded (FF), namely, simulated for time t with complexity significantly smaller than t. Shor’s algorithm provides an example of exponential cTEUR violations; we show that so do commuting local Hamiltonians and quadratic fermion Hamiltonians. A general FF method is ruled out, but finding further examples, as well as experimental demonstrations, are left for future work. We discuss possible connections to sensing and quantum gravity. This work initiates a rigorous theory of efficiency versus accuracy in energy measurements using computational complexity language.

Date: 2017
References: Add references at CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://www.nature.com/articles/s41467-017-01637-7 Abstract (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:nat:natcom:v:8:y:2017:i:1:d:10.1038_s41467-017-01637-7

Ordering information: This journal article can be ordered from
https://www.nature.com/ncomms/

DOI: 10.1038/s41467-017-01637-7

Access Statistics for this article

Nature Communications is currently edited by Nathalie Le Bot, Enda Bergin and Fiona Gillespie

More articles in Nature Communications from Nature
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().